Narrow Results

The wind-resistant performance of cable-stayed bridges under construction deteriorates sharply as the cantilever length increases, and the arrangement of the temporary pier is an effective measure to improve aerodynamic stability. To investigate the effect of the temporary pier on buffeting response of a long-span three-tower cable-stayed bridge under construction, the nonlinear buffeting analysis and wind tunnel test of aeroelastic model methods are adopted in this paper. The influence of the type and arrangement positions of temporary piers on mean wind response and the nonlinear buffeting response of double-cantilever construction are studied, and the arrangement of the temporary pier is optimized based on the buffeting response. The results show that the reduction rates of the RMS of the torsional moment at the tower bottom and the lateral buffeting displacement at the girder end with the rigid pier are 35.6% and 59.2% compared to those without the temporary pier. Further, the buffeting response will decrease as the distance between the rigid pier and the tower increases in the state. On the contrary, in the double-cantilever construction state before the constraint of temporary piers, the buffeting response will become significant as the distance increases. Therefore, it is necessary to consider the buffeting response under two construction states when optimizing the arrangement position of the temporary pier.

The excessive main girder displacement responses of the large-span cable-stayed bridges during seismic events may precipitate collisions between the main girder and the approach bridge. The viscous dampers (VDs) have been extensively employed in the seismic response control of long-span bridges, yet their effectiveness is limited. To augment the seismic-induced vibration control performance of the VD, inerter element, negative stiffness (NS) element, and spring element have been incorporated into the VD to achieve energy dissipation capacity enhancement. The equations of motion for the simplified cable-stayed bridge-damper systems are established under stochastic seismic excitation, and the design parameters of inerter and NS-based damper are optimized by using the genetic algorithm. The seismic control performance of the VD and five types of dampers are systematically compared, demonstrating that these dampers can substantially enhance the main girder displacement mitigation performance in cable-stayed bridges. Owing to the NS characteristics attributes of the inerter element and NS element and the tuning effect of the spring element, the tuned viscous mass damper (TVMD) with NS achieves a 24.56% higher efficiency in control performance compared to the VD.

To excite sufficient vibrations of bridges for more effective modal experiments to take place, traveling vehicles were utilized in many bridge field inspection campaigns in history. However, the dynamics of a bridge subjected to the traveling vehicles are of changed resonant properties compared with those of the same structure with the ambient excitation in nature. Therefore, the field modal experiments employing vehicle excitations might unfavorably lead to shifted measurement results of low-order natural frequencies for long-span bridges of large mass. Using Xinjiang Bridge (a single-tower pre-stressed concrete cable-stayed bridge with spans $40\mathrm{\text{m}}+150\mathrm{\text{m}}+150\mathrm{\text{m}}+40\mathrm{\text{m}}$) as the engineering background, this paper validates this technical notion based on reliable physical experiments and numerical simulations and seeks a practical approach to deal with the issue. It is found that the maximum deviation between the low-order modal frequencies measured on Xinjiang Bridge for the vehicle excitation case and those measured for the ambient excitation case (the accurate values) reaches 0.65Hz, and the deviation between the lower limit of the usual vehicle excitation’s energy band and the modal frequency measured (factor 1) and the traveling vehicles’ speed (factor 2) are the two key factors influencing the modal frequency shifts. An empirical model to compensate for modal frequencies’ deviations is formulated considering the two key factors accordingly, which is of high-practical significance in future applications of the modal experiments using vehicle excitations to other long-span bridges.

A procedure for the spectral analysis of buffeting response of long span bridges under unsteady wind loads is developed, with emphasis placed on inclusion of the multi-mode vibrations. The effect of mean wind velocity is considered through the aerodynamic stiffness and damping matrices using the flutter derivatives, while the effect of buffeting through the auto- and cross-power spectral densities. Compared with the conventional approach, the present approach is featured by the fact that no selection has to be made concerning the dominant modes. It can be reasonably used in analyzing cable-stayed bridges of complex geometry or of asymmetric shape, such as the Kao-Ping-Hsi Bridge, where the conventional approach has its limitations. The numerical studies indicate that using the conventional approach, by which the coupling effect is ignored, may significantly overestimate the critical wind velocity, while underestimating the buffeting responses of cable-stayed bridges.

This paper investigates the effectiveness of elastomeric and sliding types of isolation systems for the seismic response control of cable-stayed bridges. A simplified two-dimensional lumped-mass finite-element model of the Quincy Bay-view Bridge at Illinois was developed for the investigation. The seismic isolation of cable-stayed bridges is achieved using three different isolators, namely, high damping rubber bearings (HDRB), lead rubber bearings (LRB) and friction pendulum system (FPS). Time history analysis is performed for the bridge with four different earthquake ground motions applied in the longitudinal direction using Newmark's method with linear variation of acceleration over the time interval. The seismic response of the isolated cable-stayed bridge is compared with that of the bridge with no isolation system. The results show that the isolation systems are effective for reducing the absolute acceleration of the deck and the base shear response of the tower. Further, a parametric study is performed by varying the damping ratio, yield strength and friction coefficient of HDRB, LRB and FPS to investigate the influence of these parameters on the seismic response of the bridge. From such a study, optimal values can be found for the isolators for reducing the bridge responses.

This paper presents a two-node catenary cable element for the analysis of three-dimensional cable-supported structures. The stiffness matrix of the catenary cable element was derived as the inverse of the flexibility matrix, with allowances for selfweight and pretension effects. The element was then included, along with the beam and truss elements, in a geometric nonlinear analysis program, for which the procedure for computing the stiffness matrix and for performing iterations was clearly outlined. With the present element, each cable with no internal joints can be modeled by a single element, even for cables with large sags, as encountered in cable nets, suspension bridges and long-span cable-stayed bridges. The solutions obtained for all the examples are in good agreement with the existing ones, which indicates the accuracy and applicability of the element presented.

The purpose of this paper is to compare the design equation of Allowable Stress Design (ASD) with that of Load and Resistance Factor Design (LRFD) concerning the member stability for the economic design of cable-stayed bridges. Both elastic and inelastic buckling analyses are carried out for the cable-stayed bridges with the effective buckling lengths of the key members calculated. The axial-flexural interaction equations prescribed in ASD and LRFD are used to check the stability of main members in cable-stayed bridges. Parametric studies are performed for the bridges with a center span of 300, 600, 900, and 1200 m of different girder depths. Peak values of the interaction equations are calculated at the intersection between the girder and towers. Since the peak values of the interaction equations by inelastic buckling analysis are less than those by elastic buckling analysis, a more economical design of the girder and towers can be achieved using the inelastic buckling analysis. In addition, the use of LRFD specifications can result in a more economical design by about 20% on average than the ASD specifications for steel cable-stayed bridges.

To determine its actual dynamic responses under the wind loads, modal identification from the field tests was carried out for the Kao Ping Hsi cable-stayed bridge in southern Taiwan. The dynamic characteristics of the bridge identified by a continuous wavelet transform algorithm are compared with those obtained by the finite element analysis. The finite element model was then modified and refined based on the field test results. The results obtained from the updated finite element model were shown to agree well with the field identified results for the first few modes in the vertical, transverse, and torsional directions. This has the indication that a rational finite element model has been established for the bridge. With the refined finite element model, a nonlinear analysis in time domain is employed to determine the buffeting response of the bridge. Through validation of the results against those obtained by the frequency domain approach, it is confirmed that the time domain approach adopted herein is applicable for the buffeting analysis of cable-stayed bridges.

The objective of this study is to thoroughly investigate the dynamic characteristics of the Kao Ping Hsi Bridge located in southern Taiwan. A one-element cable system (OECS) and a multi-element cable system (MECS) are presented for simulating the dynamic properties of the cables of the bridge. By a finite element computation procedure, the initial shape, modal, and seismic analyses are conducted for the bridge using either the OECS or MECS model. A hybrid method combining both the two-loop iteration and the catenary function is proposed to determine the initial shapes using the MECS model. Convergent and smooth initial shapes can be obtained using such a method. The results indicate that the OECS model can yield solution in an efficient way, whereas the MECS model should be used if solutions of greater accuracy are desired.

A cable-stayed bridge model was made based on the design drawings of Shandong Binzhou Yellow River Highway Bridge (BZB) and detailed model tests were conducted. In the tests, the cable damage effects on the loading behavior and dynamic performance of the bridge model were studied by considering different cable damages' locations, different numbers of damaged cables, and different damaged levels of cables etc. The experimental results revealed that the cable damages may significantly affect the internal forces of other cables and the stress distributions of the girders; however, they have less influence on the natural frequencies of the bridge model. In parallel with the model tests, a finite element model of the bridge structure has been established. Numerical analysis for the bridge model with cable damages was carried out to validate the experimental results and explain the phenomena observed in the model tests.

This paper is concerned with mitigating multimode buffeting of cable-stayed bridges by optimizing the placements of active tuned mass dampers (ATMDs) and sensors and developing a control model and schemes. The Third Nanjing Bridge over the Yangtze River was used to formulate a mathematical control model with distributed ATMDs under wind action. Hankel norms were combined with structural mode analysis to build placement indices of the ATMDs and sensors under a defined objective while considering the influence of exterior excitation. A selection index of modes was proposed. ATMD/sensor placement on the Third Nanjing Bridge and mode selection were simulated to determine the wind response control. A control design model with accurate mode selection was developed using modal superposition and it was used to investigate control schemes of distributed ATMDs for buffeting response control of the cable-stayed bridge. The results showed that the dynamic characteristics of the developed control design model agreed well with those of the original system model. Control scheme selection depends on the tradeoff between the control objective and actuator performance. Considering realistic engineering constraints, the distributed ATMDs are shown to perform well.

The main objective of this work is to develop an active damping system that can be used to reduce the vibrations of cables in stayed bridges. As a first stage, a laboratory physical scale model of a prestressed cable was used to characterize and test the dynamic performance of the damping system that comprises accelerometers to measure cable vibrations, an electromagnetic actuator which interacts with the cable to compensate for externally induced vibrations, and a digital controller in which control strategies and algorithms are defined. In the experiment, an additional actuator was used to excite vibration disturbances on the cable modifying its frequency and amplitude, and the location for the accelerometers was defined from simulations with a linear model of the cable to optimize the damping control method. Two different system identification approaches were used to calculate the frequency response function of the whole system (cable, accelerometers and actuators); the first approach used the spectral analysis to get initial dynamic results of the cable system, while the second employed the parametric identification to obtain the transfer function of the system, by which different models were assessed. Model reduction techniques and the direct synthesis approach were selected to get a second-order model for the controller. The active damping system was first evaluated with simulation studies and then, in the laboratory. Results show that the damping system reduces the vibration amplitude up to 50% for the resonance frequency. Complementary simulations using a full scale cable model of the stayed bridge with an equivalent active damping system, showed the same damping efficiency as for that in the laboratory experiment; however, a practical application must consider the scaling factor and the limitations of possible locations and orientations of the damping actuator to get the best dynamic performance.

Cable-stayed bridges have been developing rapidly in the last decade and have become one of the most popular types of long-span bridges. One of the important issues in the design and analysis of cable-stayed bridges is determining the pre-tensioning cable forces that optimize the structural performance of the bridge. Appropriate pre-tensioning cable forces improve the damaging effect of unbalanced loading due to the deck dead load. Because the cable-stayed structure is a highly undetermined system, there is no unique solution for directly calculating the initial cable forces. Numerous studies have been conducted on the specification of cable pre-tensioning forces for cable-stayed bridges. However, most of the proposed methods are limited in their ability to optimize the structural performance. This paper presents an effective multi-constraint optimization strategy for cable-stayed bridges based on the application of an inverse problem through unit load method (ULM). The proposed method results in less stresses in the bridge members, more stability and a shorter simulation time than the existing approaches. The finite element (FE) model of the Tatara Bridge in Japan is considered in this study. The results show that the proposed method successfully restricts the pylon displacement and establishes a uniform deck moment distribution in the simulated cable-stayed bridge; thus, it might be a useful tool for designing other long-span cable-stayed bridges.

Introduced herein is a new structural damping identification approach based on a two-dimensional (2D) amplitude and phase estimation (APES) method. The original APES method is suitable for application to an undamped and complex harmonic vibration signal. Hence, it has to be modified for application to real damped vibration signals such as the vibration test signals in engineering structures. This modified approach will be named as dr_APES. It can transform one-dimensional (1D) signals in time domain into their corresponding signals in the 2D domain of frequency and damping factor. By applying this dr_APES approach, the three-dimensional (3D) amplitude spectrum, with peaks corresponding to the vibration modes, can be obtained for any given vibration signals. By accurately locating the coordinates of the peaks, modal frequencies and damping factors can be identified. Owing to the high-resolution of the location of 2D ordinates of the spectral line and the value of spectrum, the accurate location of peaks can be estimated, and therefore, the modal frequencies and damping factor can be accurately determined. This is demonstrated by a numerical case study. Moreover, by applying the proposed approach to a real onsite dynamic test on two cables in a cable-stayed bridge, the inherent damping of the two cables was identified accurately, thereby verifying the ability of proposed damping identification approach in meeting the requirement of weak damping characteristics identification in flexible structures such as naked cables.

In order to evaluate the dynamic response of the train running on long-span cable-stayed bridges under uniform seismic excitations, a time-domain framework of analysis for the train–bridge system is established. The rail irregularities are treated as internal excitation and seismic loads as external excitation considering the inertia forces induced by the 3D seismic waves. The vehicles are modeled as mass-spring-damper systems, and the cable-stayed railway bridge is simulated by finite elements. A comprehensive analysis of the train–bridge system subjected to earthquake is conducted, focused on the effect of seismic ground motions on the dynamic response of the running train. Four kinds of seismic waves, each with three components, are simulated, with their spectral characteristics taken into account. To consider the stochastic characteristic of actual seismic waves, the effect of the incident angle and occurrence time of earthquakes on the bridge and vehicles is analyzed. Moreover, the earthquakes with various occurrence probability levels are also studied and the safety of the train running under the seismic action is evaluated, which may be used as the operation reference for the railway authority. The results demonstrate that the seismic ground motions have significant effects on the dynamic response of railway vehicles running on the long-span cable-stayed bridge under various spectrum characteristics, incident angles, occurrence times, and occurrence probabilities.

This paper discusses the necessity of considering the concurrent effects of uniform temperature and earthquake loadings in the design of cable-stayed bridges. This load combination is not foreseen in current design standards such as AASHTO and Eurocode. Three-dimensional finite element models of cable-stayed bridges are employed for nonlinear time history analyses. A load combination is proposed that adds uniform temperature loading to the existing extreme event load combination. The proposed combination is compared with existing extreme event load combination and the changes in forces and displacements are noted. A parametric study is then conducted by varying a number of properties of the cable-stayed bridges such as, span length, shape of the pylon, the deck/pylon connection and the actual temperature load. Pylon reactions and the deck axial forces are found to be more vulnerable to concurrent loadings for cable-stayed bridges of longer spans.

The paper is aimed at investigating the longitudinal vibration and vibration reduction of a cable-stayed bridge under vehicular loads with emphasis on the longitudinal resonance. To investigate the phenomenon of longitudinal resonant vibration, the equivalent longitudinal excitation for the bridge deck due to moving vertical loads is approximately expressed as longitudinal loads with a sine-wave form. A formula for estimating the longitudinal resonant speed of the cable-stayed bridge is developed. A long-span cable-stayed railway bridge is considered in the case study to calculate the longitudinal response of the bridge under moving loads at different speeds. The numerical results indicate that the longitudinal resonance for the cable-stayed bridge occurs when the speeds of the moving loads approach the resonant speed predicted by the analytical formula. A fluid viscous damper (FVD) is employed to reduce the longitudinal vibration of the bridge under moving loads. The results show that the longitudinal resonant responses of the cable-stayed bridge can be effectively mitigated by the FVD adopted.

Modal identification aims at identifying the dynamic properties including natural frequency, damping ratio, and mode shape, which is an important step in further structural damage detection, finite element model updating, and condition assessment. This paper presents the work on the investigation of the dynamic characteristics of a long-span cable-stayed bridge-Sutong Bridge by a Bayesian modal identification method. Sutong Bridge is the second longest cable-stayed bridge in the world, situated on the Yangtze River in Jiangsu Province, China, with a total length of 2 088m. A short-term nondestructive on-site vibration test was conducted to collect the structural response and determine the actual dynamic characteristics of the bridge before it was opened to traffic. Due to the limited number of sensors, multiple setups were designed to complete the whole measurement. Based on the data collected in the field tests, modal parameters were identified by a fast Bayesian FFT method. The first three modes in both vertical and transverse directions were identified and studied. In order to obtain modal parameter variation with temperature and vibration levels, long-term tests have also been performed in different seasons. The variation of natural frequency and damping ratios with temperature and vibration level were investigated. The future distribution of the modal parameters was also predicted using these data.

There have been numerous experimental studies on the seismic collapse of reinforced concrete (RC) buildings and RC girder bridges, but not on the seismic collapse of RC pedestrian cable-stayed bridges. Postearthquake field investigations revealed that if RC pedestrian cable-stayed bridges in seismic regions were not appropriately designed, they are likely to encounter severe damage or collapse. This paper thus presents an experimental investigation on a 1:12 scaled RC pedestrian cable-stayed bridge to explore the seismic behavior and collapse mechanism of the bridge under different levels of ground motion. The design, construction, and installation of the bridge, along with the shake table tests, were performed. The dynamic characteristic tests of the bridge were carried out, with the natural periods and mode shapes identified. The bridge was then tested by subjecting it to three levels of ground motion, i.e. small, moderate and large earthquakes. The seismic behavior and seismic-resistant capacity of the cable-stayed bridge were finally assessed at the component level and the failure mode of the bridge was identified based on the seismic responses recorded by the measurement system. The test results showed that the collapse of the RC pedestrian cable-stayed bridge was triggered from the flexure failure of its columns and ended with the flexure-shear failure of its tower.

The presence of intermediate supports usually imposes difficulties in identifying the tension force of stayed cables in cable-stayed bridges or hanger cables in arch bridges. This paper establishes the partial differential equations of motion of the cable and derives two numerical models with (Model 1) and without (Model 2) considering the flexural rigidity. The effects of two intermediate supports on the identification accuracy of the cable tension force are further studied analytically and experimentally. The effects of several non-dimensional parameters (e.g. damper location, support stiffness, flexural rigidity, and mode order of the cable) on the identification accuracy of the models are also investigated. It is theoretically concluded that the simplified Model 2 provides acceptable accuracy on tension force identification when the non-dimensional parameter $\xi$ is greater than 90 (slender cables), whereas the accurate Model 1 can be applied for tension force identification at any scenarios. The feasibility of two models is further verified by three numerical examples and field tests on two real-world arch bridges.